Question

solve the equation In(x+9)-In(x-5)=In(x+7)-In(x-4).

Answer 1

using the law of logarithms, this can be simplified to
\[\ln (x+9/x-5)=\ln (x+7/x-4)\]

Answer 2

If we exponentiate both sides of the equation by e our new equation will be
x+9/x-5=x+7/x-4

Answer 3

multiply both sides of the equation by x-5 to get
x-9=(x+7)(x-5)/(x-4)

Answer 4

then multiply both sides of the equation by x-4 to get
(x-9)(x-4)=(x+7)(x-5)

Answer 5

do you mean (x+9)?

Answer 6

woops thanks for that.
now we can use the FOIL method to simplify our equation
(x+9)(x-4)=x^2+5x-36
(x+7)(x-5)=x^2+2x-35
so our simplified equation is
x^2+5x-36=x^2+2x-35

Answer 7

so there is really no solution for this problem?

Answer 8

subtract x^2+2x-35 from both sides to get...
3x-1=0
solving for x we get,
3x=1
x=1/3

Answer 9

okay thanks! That was one of the possibly answers but, the answer key says no solution ?

Answer 10

I don't see how the answer key says the equation has no solution unless they solved it a different way

Answer 11

yes, I just think maybe they made a mistake?

Answer 12

But thank you for helping me! I know how to use your steps for other problems like this! thanks!!!

Answer 13

Your're very welcome!! xD